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Math Help - absolute value proof

  1. #1
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    absolute value proof

    How do i prove the following using the properties of absolute values?

    A) |x|^2 = x^2

    B) |x| = sqrt{ x^2}

    Thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by MagicS06 View Post
    How do i prove the following using the properties of absolute values?

    A) |x|^2 = x^2

    B) |x| = sqrt{ x^2}

    Thanks
    For both you can use the fact that:

    |x| = \left \{ \begin{array}{cc}x, &\mbox { if } x \geq 0\\-x, &\mbox { if } x < 0 \end{array}\right.

    and show that the functions on the right satisfy the same function. Part B is actually an alternative definition for |x|
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